Breakdown of quasilocality in long-range quantum lattice models.

Area of Science:

• Quantum physics
• Condensed matter theory
• Statistical mechanics

Background:

• Understanding quantum correlation dynamics is crucial for quantum information science.
• Long-range interactions in quantum systems challenge traditional locality assumptions.
• The Lieb-Robinson bound provides a fundamental limit on the speed of quantum information propagation.

Purpose of the Study:

• To investigate the necessity and sufficiency of power-law decay for correlation spreading in quantum lattice models.
• To explore the emergence of causal regions and supersonic propagation under long-range interactions.
• To analyze the behavior of quantum channels and correlation functions in systems with varying interaction decay rates.

Main Methods:

• Analytical treatment of long-range Ising models.
• Application of quantum metrology tools to construct specific Hamiltonians.
• Numerical simulations using matrix product state (MPS) methods for the XXZ spin chain.

Main Results:

• Power-law decay of interactions is shown to be a necessary condition for Lieb-Robinson-type bounds.
• For interaction exponents smaller than lattice dimensionality, causal regions can disappear, leading to distance-independent correlations.
• Supersonic correlation propagation is observed, with spreading following a power law rather than exponential increase.

Conclusions:

• The study establishes the critical role of interaction decay exponents in defining the causal structure of quantum systems.
• Non-equilibrium dynamics can exhibit phenomena beyond the standard Lieb-Robinson bound, such as supersonic propagation.
• Findings have implications for quantum communication, computation, and understanding complex quantum many-body systems.